Question: Simplify the following expression: $r = \dfrac{96x - 108}{-48}$ You can assume $x \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $96x - 108 = (2\cdot2\cdot2\cdot2\cdot2\cdot3 \cdot x) - (2\cdot2\cdot3\cdot3\cdot3)$ The denominator can be factored: $-48 = - (2\cdot2\cdot2\cdot2\cdot3)$ The greatest common factor of all the terms is $12$ Factoring out $12$ gives us: $r = \dfrac{(12)(8x - 9)}{(12)(-4)}$ Dividing both the numerator and denominator by $12$ gives: $r = \dfrac{8x - 9}{-4}$